derivative of (sin(x)/(cos^3(x)))

解答

\frac{d}{d x} (\frac{sin ( x )}{cos ^{3} ( x )})

sec^{2} (x) (1 + 3 tan^{2} (x))

求解步骤

\frac{d}{d x} (\frac{sin ( x )}{cos ^{3} ( x )})

化简

\frac{sin ( x )}{cos ^{3} ( x )} : sec^{3} (x) sin (x)

= \frac{d}{d x} (sec^{3} (x) sin (x))

使用微分乘法定则:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = sec^{3} (x), g = sin (x)

= \frac{d}{d x} (sec^{3} (x)) sin (x) + \frac{d}{d x} (sin (x)) sec^{3} (x)

\frac{d}{d x} (sec^{3} (x)) = 3 sec^{3} (x) tan (x)

\frac{d}{d x} (sin (x)) = cos (x)

= 3 sec^{3} (x) tan (x) sin (x) + cos (x) sec^{3} (x)

化简

3 sec^{3} (x) tan (x) sin (x) + cos (x) sec^{3} (x) : sec^{2} (x) (1 + 3 tan^{2} (x))

= sec^{2} (x) (1 + 3 tan^{2} (x))

n = 1 \sum \infty \frac{6}{n ^{3}}

x \to 1 lim (\frac{x ^{3} - 1}{x - 1})

\int (\frac{1}{5})^{x} d x

\frac{\partial}{\partial x} (arcsin (6 x yz))

d er i v a t i v e (3 t + 4) \cdot sin (π (\frac{t}{3} - 0.5))